Models of sensor operations for border surveillance

This article is motivated by the diverse array of border threats, ranging from terrorists to arms dealers and human traffickers. We consider a moving sensor that patrols a certain section of a border with the objective to detect infiltrators who attempt to penetrate that section. Infiltrators arrive according to a Poisson process along the border with a specified distribution of arrival location, and disappear a random amount of time after their arrival. The measures of effectiveness are the target (infiltrator) detection rate and the time elapsed from target arrival to target detection. We study two types of sensor trajectories that have constant endpoints, are periodic, and maintain constant speed: (1) a sensor that jumps instantaneously from the endpoint back to the starting‐point, and (2) a sensor that moves continuously back and forth. The controlled parameters (decision variables) are the starting and end points of the patrolled sector and the velocity of the sensor. General properties of these trajectories are investigated. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

模糊随机过程的可分性与可测性

本文证明了一个模糊随机过程{_t(ω)t∈T}必存在一个与之等价的可分模糊随机过程{_t(ω)t∈T};且若模糊随机过程{_t(ω)t∈T}随机连续,则它存在等价的,可分且可测的模糊随机过程{■_t(ω)t∈T}。     

误差随机过程的一种数据预处理方法

在数据连续采集过程中,误差是一个随机的过程,有的误差数据出现“失真”,本文结合指挥仪综合检测中动态误差情况,提出一种平稳误差过程和非平稳误差过程的数据预处理方法。     

The (s,Q) inventory model with Erlang lead time and deterministic demand

We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead‐time distribution, and another where we have no information, except for computer‐generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead‐time distribution is available and 97.54–99.09% when only computer‐generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near‐optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

坦克分队遭遇战斗火力运用研究

根据遭遇战斗的特点,运用随机格斗、微分对策数理战术模型,研究坦克分队遭遇战斗最优火力运用策略问题.研究得出的结论符合坦克分队战术特点,为坦克分队指挥决策提供辅助作用.     

Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming

The purpose of this paper is to investigate the problem of constructing an appointment template for scheduling patients at a specific type of multidisciplinary outpatient clinic called an integrated practice unit (IPU). The focus is on developing and solving a stochastic optimization model for a back pain IPU in the face of random arrivals, an uncertain patient mix, and variable service times. The deterministic version of the problem is modeled as a mixed integer program with the objective of minimizing a weighted combination of clinic closing time (duration) and total patient waiting time (length of stay). A two‐stage stochastic program is then derived to account for the randomness and the sequential nature of the decisions. Although it was not possible to solve the two‐stage problem for even a limited number of scenarios, the wait‐and‐see (WS) problem was sufficiently tractable to provide a lower bound on the stochastic solution. The introduction of valid inequalities, limiting indices, and the use of special ordered sets helped to speed up the computations. A greedy heuristic was also developed to obtain solutions much more quickly. Out of practical considerations, it was necessary to develop appointment templates with time slots at fixed intervals, which are not available from the WS solution. The first to be derived was the expected value (EV) template that is used to find the expected value of the EV solution (EEV). This solution provides an upper bound on the objective function value of the two‐stage stochastic program. The average gap between the EEV and WS solutions was 18%. Results from extensive computational testing are presented for the EV template and for our adaptation of three other templates found in the literature. Depending on the relative importance of the two objective function metrics, the results demonstrate the trade‐off that exists between them. For the templates investigated, the “closing time” ranged from an average of 235 to 275 minutes for a 300‐minute session, while the corresponding “total patient time in clinic” ranged from 80 to 71 minutes.     

A decomposition algorithm applied to planning the interdiction of stochastic networks

We describe the application of a decomposition based solution method to a class of network interdiction problems. The problem of maximizing the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain is shown to be solved effectively by applying a scenario decomposition method developed by Riis and Schultz [Comput Optim Appl 24 (2003), 267–287]. Computational results demonstrate the effectiveness of the algorithm and design decisions that result in speed improvements. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

基于随机虚拟样机的某型自行火炮扭力轴动力仿真

依据随机动力学、多体系统动力学和数理统计理论,借助MSC\Adams仿真软件和MATLAB工具,提出随机虚拟样机的概念。并以某型自行火炮的扭力轴为例,在建立的虚拟样机上,实现不确定性因素下从底盘整体到悬挂系统、再到扭力轴的动力仿真。     

一类搜索型多对二随机格斗的获胜概率

研究搜索型多对二随机格斗战斗模型。假设格斗开始时A方有m件武器,B方有2件武器,B方处于隐蔽状态,格斗开始后B方可以直接对A方进行射击,A方需先搜索到B方后才能进行射击。双方各为同类武器,都是集火射击,所有开火都是独立的,每件武器开火射击直到毁伤对方才重新射击下一个目标。对搜索时间和毁伤间隔时间都服从一般分布的随机格斗模型,通过分析各状态的特征,利用状态概率分析方法和向后递归时间方法建立状态方程,求出了格斗处在各个状态的概率,并得到双方的获胜概率计算公式。     

Partial equilibrium in risk‐based production decisions

Characteristically, a small subset of operational problems admit risk neutrality when contingent claims methodology were used in their analysis. That is, for the majority of manufacturing and production problems, operating cash flows are not directly linked to prices of traded assets. However, to the extent that correlations can be estimated, the methodology's applicability to a broader set of operational problems is supported. Our article addresses this issue with the objective of extending the use of contingent claims techniques to a larger set of operational problems. In broad terms, this objective entails a partial equilibrium approach to the problem of valuing uncertain cash flows. To this end, we assume risk aversion and cast our approach within Merton's intertemporal capital asset pricing model. In this context, we formulate a “generic” production valuation model that is framed as an exercise in stochastic optimal control. The model is versatile in its characterization and can easily be adapted to accommodate a wide‐ranging set of risk‐based operational problems where the underlying sources of uncertainty are not traded. To obtain results, the model is recast as a stochastic dynamic program to be solved numerically. The article addresses a number of fundamental issues in the analysis risk based decision problems in operations. First, in the approach provided, decisions are analyzed under a properly defined risk structure. Second, the process of analysis leads to suitably adjusted probability distributions through which, appropriately discounted expectations are derived. Third, through consolidating existing concepts into a standard and adaptable framework, we extend the applicability of contingent claims methodology to a broader set of operational problems. The approach is advantageous as it obviates the need for exogenously specifying utility functions or discount rates.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011